30 research outputs found
Smooth and fast versus instantaneous quenches in quantum field theory
We examine in detail the relationship between smooth fast quantum quenches,
characterized by a time scale , and {\em instantaneous quenches},
within the framework of exactly solvable mass quenches in free scalar field
theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols
remain distinct in the limit because of the relation
of the quench rate to the UV cut-off, i.e., always holds
in the fast smooth quenches while for instantaneous
quenches. Here we study UV finite quantities like correlators at finite spatial
distances and the excess energy produced above the final ground state energy.
We show that at late times and large distances (compared to the quench time
scale) the smooth quench correlator approaches that for the instantaneous
quench. At early times, we find that for small spatial separation and small
, the correlator scales universally with , exactly as in
the scaling of renormalized one point functions found in earlier work. At
larger separation, the dependence on drops out. The excess energy
density is finite (for finite ) and scales in a universal fashion
for all . However, the scaling behaviour produces a divergent result in the
limit for , just as in an instantaneous
quench, where it is UV divergent for . We argue that similar results
hold for arbitrary interacting theories: the excess energy density produced is
expected to diverge for scaling dimensions .Comment: 52 pages; v2: minor modifications to match published versio
An exactly solvable quench protocol for integrable spin models
Quantum quenches in continuum field theory across critical points are known
to display different scaling behaviours in different regimes of the quench
rate. We extend these results to integrable lattice models such as the
transverse field Ising model on a one-dimensional chain and the Kitaev model on
a two-dimensional honeycomb lattice using a nonlinear quench protocol which
allows for exact analytical solutions of the dynamics. Our quench protocol
starts with a finite mass gap at early times and crosses a critical point or a
critical region, and we study the behaviour of one point functions of the
quenched operator at the critical point or in the critical region as a function
of the quench rate. For quench rates slow compared to the initial mass gap, we
find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to
the mass gap, but slow compared to the inverse lattice spacing, we find scaling
behaviour similar to smooth fast continuum quenches. For quench rates of the
same order of the lattice scale, the one point function saturates as a function
of the rate, approaching the results of an abrupt quench. The presence of an
extended critical surface in the Kitaev model leads to a variety of scaling
exponents depending on the starting point and on the time where the operator is
measured. We discuss the role of the amplitude of the quench in determining the
extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the
saturation.Comment: 54 pages, 13 figures; v2: added analytic argument for Kitaev mode
Dynamics of holographic thermalization
Dynamical evolution of thin shells composed by different kinds of degrees of freedom collapsing within asymptotically AdS spaces is explored with the aim of investigating models of holographic thermalization of strongly coupled systems. From the quantum field theory point of view this corresponds to considering different thermal quenches. We carry out a general study of the thermalization time scale using different parameters and space-time dimensions, by calculating renormalized space-like geodesic lengths and rectangular minimal area surfaces as extended probes of thermalization, which are dual to two-point functions and rectangular Wilson loops. Different kinds of degrees of freedom in the shell are described by their corresponding equations of state. We consider a scalar field, as well as relativistic matter, a pressureless massive fluid and conformal matter, which can be compared with the collapse of an AdS-Vaidya thin shell. Remarkably, in the case of AdS5, for conformal matter, the thermalization time scale becomes much larger than the others. Furthermore, in each case we also investigate models where the cosmological constants of the inner and outer regions separated by the shell are different. We found that in this case only a scalar field shell collapses, and that the thermalization time scale is also much larger than the AdS-Vaidya case.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica
De Sitter Horizons & Holographic Liquids
We explore asymptotically AdS solutions of a particular two-dimensional
dilaton-gravity theory. In the deep interior, these solutions flow to the
cosmological horizon of dS. We calculate various matter perturbations at
the linearised and non-linear level. We consider both Euclidean and Lorentzian
perturbations. The results can be used to characterise the features of a
putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is
assessed through the soft mode action at the AdS boundary, as well as the
behaviour of shockwave type solutions.Comment: 37 pages, 7 figures; v2: minor corrections; v3: updated references,
new Penrose diagram and minor comments added to match published version; v4:
Acknowledgement adde
Renormalisation Group Flows of the SYK Model
We explore computationally tractable deformations of the SYK model. The
deformed theories are described by the sum of two SYK Hamiltonians with
differing numbers, and , of interacting fermions. In the large
limit, employing analytic and numerical tools, we compute finite
temperature correlation functions and thermodynamic quantities. We identify a
novel analytically solvable RG flow in the large limit. We find that, under
certain circumstances, the RG flow in the strongly coupled infrared phase
exhibits two regions of linear-in-temperature entropy, which we interpret in
terms of Schwarzian actions. Using conformal perturbation theory we compute the
leading relevant correction away from the intermediate near-conformal fixed
point. Holographic spacetimes in two spacetime dimensions that reproduce the
thermodynamics of the microphysical theory are discussed. These are flow
geometries that interpolate between two Euclidean near-AdS spacetimes with
different radii. The Schwarzian soft mode corresponding to the AdS region
in the deep interior resides entirely within the geometric regime.Comment: 27 pages plus appendices, 16 figure
Comments on Jacobson’s “entanglement equilibrium and the Einstein equation”
Using holographic calculations, we examine a key assumption made in Jacobson’s recent argument for deriving Einstein’s equations from vacuum entanglement entropy. Our results involving relevant operators with low conformal dimensions seem to conflict with Jacobson’s assumption. However, we discuss ways to circumvent this problem.Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Galante, Damián A.. Western University; Canadá. Perimeter Institute for Theoretical Physics; CanadáFil: Myers, Robert C.. Perimeter Institute for Theoretical Physics; Canad
Shape Deformations of Charged R\'enyi Entropies from Holography
Charged and symmetry-resolved R\'enyi entropies are entanglement measures
quantifying the degree of entanglement within different charge sectors of a
theory with a conserved global charge. We use holography to determine the
dependence of charged R\'enyi entropies on small shape deformations away from a
spherical or planar entangling surface in general dimensions. This dependence
is completely characterized by a single coefficient appearing in the two point
function of the displacement operator associated with the R\'enyi defect. We
extract this coefficient using its relation to the one point function of the
stress tensor in the presence of a deformed entangling surface. This is mapped
to a holographic calculation in the background of a deformed charged black hole
with hyperbolic horizon. We obtain numerical solutions for different values of
the chemical potential and replica number in various spacetime dimensions,
as well as analytic expressions for small chemical potential near . When
the R\'enyi defect becomes supersymmetric, we demonstrate a conjectured
relation between the two point function of the displacement operator and the
conformal weight of the twist operator.Comment: 35+16 pages, 9 figure